On optimistic, pessimistic and mixed fuzzy-programming based approaches to solve multi-objective fully intuitionistic fuzzy linear fractional programming problems

A decision-maker often encounters a state of uncertainty as well as hesitancy due to various unpredictable factors while solving real-world optimization problems. Due to ambiguity in the decision-making process, the parameters and decision variables of an optimization model generally fail to have the exact values. To deal with such realistic uncertain conditions, the concept of intuitionistic fuzzy numbers has been employed widely. In this article, a model of the linear fractional programming problem having multiple objectives with all the parameters and decision variables expressed as intuitionistic fuzzy numbers has been presented. To solve the problem, we first linearize the fractional model using appropriate transformations, and thereafter utilizing the accuracy function and intuitionistic fuzzy programming, the equivalent optimization model is obtained. The conflicting nature of the multiple objectives in the linearized model has been handled using the linear and exponential membership/non-membership functions applying normal, optimistic, pessimistic, and mixed approaches. Moreover, to validate the various equivalent constructions of the original problem, the underlying theorems are also proved at the relevant places. In last, a practical application related to production process in the textile industry has been constructed and solved using the proposed algorithm, and further, a comparison is drawn among various approaches to establish the efficacy of the proposed modelling and developed algorithm.